13.2.1 Constructing Born-Haber Cycles

• What is a Born-Haber Cycle used to relate in thermodynamics?

  Lattice energy to enthalpy
• A Born-Haber Cycle can directly measure lattice energy.

  False
• A Born-Haber Cycle uses Hess's Law to calculate the lattice energy indirectly
• Steps to construct a Born-Haber Cycle

  1️⃣ Sublimation of the metal

  2️⃣ Ionization of the metal

  3️⃣ Dissociation of the halogen

  4️⃣ Electron affinity of the halogen

  5️⃣ Formation of the ionic compound

  6️⃣ Lattice energy
• What is the general equation for calculating lattice energy in a Born-Haber Cycle?

  ΔH_{\text{formation}} = ΔH_{\text{sublimation}} + ΔH_{\text{ionization}} + ΔH_{\text{dissociation}} + ΔH_{\text{electron affinity}} + ΔH_{\text{lattice energy}}</latex>
• The lattice energy of an ionic compound is always negative.
• A Born-Haber Cycle uses Hess's Law to relate lattice energy to other enthalpy changes
• What is the relationship between the enthalpy changes in a Born-Haber Cycle?

  ΔH_{\text{formation}} = ΔH_{\text{sublimation}} + ΔH_{\text{ionization}} + ΔH_{\text{dissociation}} + ΔH_{\text{electron affinity}} + ΔH_{\text{lattice energy}}</latex>
• Match the stages of a Born-Haber Cycle with their descriptions:

  Sublimation of the metal ↔️ Conversion of metal from solid to gas

  Ionization of the metal ↔️ Removal of electrons from the metal

  Dissociation of the halogen ↔️ Breaking halogen molecules into atoms

  Electron affinity of the halogen ↔️ Addition of electrons to halogen atoms
• Which enthalpy change is associated with the breaking of halogen molecules into atoms?

  Dissociation
• The electron affinity of a halogen is always exothermic.
• Steps to construct a Born-Haber Cycle

  1️⃣ Sublimation of the metal

  2️⃣ Ionization of the metal

  3️⃣ Dissociation of the halogen

  4️⃣ Electron affinity of the halogen

  5️⃣ Formation of the ionic compound

  6️⃣ Lattice energy
• A Born-Haber Cycle is used to determine the lattice energy of an ionic compound.
• What is the enthalpy change associated with the sublimation of a metal in a Born-Haber Cycle?

  $ΔH_{\text{sublimation}}$
• Match the stage in a Born-Haber Cycle with its enthalpy change:

  Ionization of the metal ↔️ $ΔH_{\text{ionization}}$

  Electron affinity of the halogen ↔️ $ΔH_{\text{electron affinity}}$

  Formation of the ionic compound ↔️ $ΔH_{\text{formation}}$

  Lattice energy ↔️ $ΔH_{\text{lattice energy}}$
• The Born-Haber Cycle relates lattice energy to other enthalpy changes using Hess's Law.
• Order the stages of a Born-Haber Cycle based on their sequence:

  1️⃣ Sublimation of the metal

  2️⃣ Ionization of the metal

  3️⃣ Dissociation of the halogen

  4️⃣ Electron affinity of the halogen

  5️⃣ Formation of the ionic compound

  6️⃣ Lattice energy
• A Born-Haber Cycle determines the lattice energy indirectly by relating it to other enthalpy changes.
• What law is used in a Born-Haber Cycle to relate enthalpy changes?

  Hess's Law
• Match the enthalpy change in a Born-Haber Cycle with its description:

  $ΔH_{\text{dissociation}}$ ↔️ Energy required to break halogen bonds

  $ΔH_{\text{formation}}$ ↔️ Energy released when ions combine

  $ΔH_{\text{lattice energy}}$ ↔️ Energy to form crystal lattice

  $ΔH_{\text{electron affinity}}$ ↔️ Energy released when halogen gains electron
• The Born-Haber Cycle diagram is a visual representation of enthalpy changes in the formation of an ionic compound.
• The Born-Haber Cycle diagram relates lattice energy to other thermodynamic quantities using Hess's Law.
• Order the steps to draw a Born-Haber Cycle diagram:

  1️⃣ Start with the elements in their standard states

  2️⃣ Show the sublimation of the metal and dissociation of the halogen

  3️⃣ Illustrate the ionization of the metal and electron affinity of the halogen

  4️⃣ Combine the ions to form the ionic compound, representing the lattice energy

  5️⃣ Show the overall formation of the ionic compound
• What is the first step in drawing a Born-Haber Cycle diagram?

  Standard states of elements
• The ionization of the metal is illustrated in the Born-Haber Cycle diagram after sublimation and dissociation.
• The final stage in a Born-Haber Cycle diagram shows the overall formation of the ionic compound.
• What are the steps to draw a Born-Haber Cycle diagram in the correct order?

  1️⃣ Start with the elements in their standard states.

  2️⃣ Show the sublimation of the metal and dissociation of the halogen.

  3️⃣ Illustrate the ionization of the metal and electron affinity of the halogen.

  4️⃣ Combine the ions to form the ionic compound, representing the lattice energy.

  5️⃣ Show the overall formation of the ionic compound.
• The Born-Haber Cycle is related to Hess's Law
• What does the overall formation of the ionic compound represent in the Born-Haber Cycle?

  Lattice energy
• The lattice energy is always negative in the Born-Haber Cycle.
• The formation enthalpy of a compound is equal to the sum of all enthalpy changes in the Born-Haber Cycle
• What steps are involved in the Born-Haber Cycle for NaCl?

  Subliming Na, ionizing Na, dissociating Cl₂, adding an electron to Cl, and forming NaCl from Na⁺ and Cl⁻.
• What type of enthalpy change is associated with the combination of ions to form the ionic compound?

  Lattice energy
• To draw a Born-Haber Cycle diagram, start with the elements in their standard states
• The sublimation of the metal and dissociation of the halogen are steps in the Born-Haber Cycle.
• Steps to draw a Born-Haber Cycle diagram

  1️⃣ Start with the elements in their standard states

  2️⃣ Show the sublimation of the metal and dissociation of the halogen

  3️⃣ Illustrate the ionization of the metal and electron affinity of the halogen

  4️⃣ Combine the ions to form the ionic compound, representing the lattice energy

  5️⃣ Show the overall formation of the ionic compound
• The Born-Haber Cycle relates enthalpy changes through Hess's Law
• What is the formula for Hess's Law as applied in the Born-Haber Cycle?

  ΔH_{\text{formation}} = ΔH_{\text{sublimation}} + ΔH_{\text{ionization}} + ΔH_{\text{dissociation}} + ΔH_{\text{electron affinity}} + ΔH_{\text{lattice energy}}</latex>
• For NaCl, the Born-Haber Cycle includes subliming Na, ionizing Na, dissociating Cl₂, adding an electron to Cl, and forming NaCl from Na⁺ and Cl⁻.
• The sublimation of the metal corresponds to an enthalpy change denoted as ΔH_{\text{sublimation}}